Sonar ray tracer



June 28, 1960 IR. B. BLlzA'RD :Qn-AL soNAR RAY TRACER 2 Sheets-Sheet 1 Original Filed J une 11. 1954 L INPIIWNNINMN June 28, 1960 R. B. BLlzARD ETAL 2,942,782

SONAR RAY TRACER 2 Sheets-Sheet 2 Original Filed June 1l, 1954 KAG 2,942,782 soNAR RAY TRACER Robert ll. Blizard, Houston, Tex., Richard Proskauer, Westbury, N.Y., and VictonVa'cquier, La `lolla, Calif., assignors to Sperry Rand Corporation, a corporation of Delaware Continuation of application, Ser. No. 436,168, 'June 11,-10

1954. This application Jan. 26, 1955, Ser. No. 484,212

` 11 claims. (cl. zas-isz) Y This invention relates to analogue computers, and more particularly, is concerned with a computer `for tracing the paths ofunderwater sound rays Aas predicated from sound velocity versus depth data. continuation of application Serial No. 436,168, iiled June 11, 1954, and now abandoned.

Itis well known that soundrrays lemanating:from a source underwater do not follow straight lines, butare bent due to the change in velocity of the rays'at different depths. The resulting sound intensity pattern is rather complex, being made up of regions of greater sound intensity due to the convergence of a number of rays following different paths, and regions of low. intensity where substantially no r-ays may pass.A A plot-of a set of rays provides a picture of the sound field, and by plotting a large number of rays, the density of the rays at various points is an indication of the sound intensity. f

Heretofore it has been the practice toplot individual rays from measured data and computation, -but because of the tremendous amount of work required, only a few rays were plotted for each picture of a sound eld. Moreover, the number of such graphs representing dilerent depths and different conditions alecting the sound eld pattern which could be made by hand was necessarily limited. A mechanical computer and plotter was developed which was capable of tracing ten or iifteen rays an hour, which was 4a great improvement over the manual method. However, no satisfactory method has been heretofore developed for a high speed plot of a large number of rays from a source of ininitely variable depth.

It is the general object of this invention to avoid the foregoing limitations in the prior art methods by the provision of an improved sonar ray tracer whch is capable of very rapidly computing `and plotting a family of sound rays from measured `data of sound velocity, in a medium as a function of depth.

Another object of this invention is the provision Vof a sound intensity predictor producing a family of traces on a cathode ray screen corresponding to yrays of a sound field wherein the -density of vthe traces on the screen is an lindication, of the corresponding sound intensityin the f sound iield. t t

Another object of this invention is to provide anelectronic ray tracer which can be used in any type of investigation involving the propagation of ray` energy through any medium.

These and other objects of the inventionwhich will become'apparent as the description proceeds are achieved by the provision of a computer vincluding a rst integrator andsecond integrator connected in cascade. An electronic function generator Ifor producing anoutput signal that is a predetermined function of an input signal t has its input connected to the output of the second integrator and its output connected to the input of the first integrator. `The predetermined function is established vfrom velocity versus depth data. A cathode raytube is connected with its vertical deection plates coupled to the output of the second integrator and with its This application is a Patented June 28, 1960 horizontal deiiection plates coupled to the output of a Vshould b'ehad to the accompanying drawings, wherein:

Fig. 1 is a block diagram of the computer comprising the present invention;

Fig. 2 is a wiring diagram of one of the integrators together with the circuit for setting in the initial condi- OII; 1. V.

Fig. 3 is a front elevation of a mask used in the function generator of the computer; and

Fig. 4 is a graphical plot' of a typical ray used in developing the equations forV the ray paths.

The principles of the Vpresent invention can best be understood by considering a transducer located at a depth y1 below the sur-tace of the ocean, the transducer sending out sound rays over an angle in the vertical plane.

. As long as a particular sound ray travels in .a medium in which the velocity is constant, it will be directed along a straight line. However, as soon as the ray passes into a medium inwhich the velocity of propagation is dilerent, the ray will be bent and kwill proceed in the second mediumV along a different line. This phenomenon is known as Snells law of refraction, which is expressed mathematically:

cos 01 cos @M l where V, is Vthe velocity in a rst medium, V@ Vthe vedy @dan 0f=y (-2) and the rate of change of slope is 2y d tan 0 at: a 3) where 6 is the angle with horizontal made by a tangent to the ray curve at the point (x, y)- lAccording to Snells law,as above stated in Equation l,

cos 0=kV (4) Solving for y in terms of V by using Equations 2 and 4,

Y sin 0 "y/1--cos2 'cw/l-(ltV)2 y tan cos cos 0 y kV, (5) Taking the derivative of Equation 5 gives W: 1VV iat/ 1 1dV omit-f '5:0052 o This is a general equation for the path of a ray in terms of depth versus distance. Y

' To simplify the solution of Equation 6 it may be as'- sumed that only rays making small angles to thehorizontal are to be plotted, so that cos2 0 is approximately equal to unity. Since it is easier to use time as the independent variable in any computer, Equation 6 is fur- 3 ther simplified by th'e assumption that the component of velocity of the ray in the horizontal direction is substantially constant. This assumption is valid since the velocity actually varies only slightly at different depths, so that the average velocity Vav may be used. Thus x becomes proportional` to time, as expressed in the This equation establishes that the rate of change of slope 11 of a particular ray is proportional to the ver- -tical rate of change of velocity divided by the velocity V.

The velocity of sound in the sea as function of depth for various conditions has been established by bathothermograph measurements which are available in the form of published charts. By utilizing this information the computer of the present invention provides a solution of Equation of depth y (for a ray having any selected initial condition of depth and angle) as a function of time, the computer presenting the solution as a Vtrace on a cathode ray tube.

Referring to the block diagram of the computer in Fig. 1, the numeral 10 indicates generally a function generator which is preferably of a type described in the article Photoelectric Waveform Generator, by D. E. Sunstein, Electronics, February 1949, page 100. The function generator is capable of producing a singlevalue transfer characteristic Vfrom al simple mask. It includes a cathode ray tube 12in front of which is positioned an opaque mask 14. The shape and method of forming the mask will be hereinafter more particularly described. A phototube 16 feeds a servo amplifier 18, the output of which is coupled to the vertical deflection plates of the Ycathode ray tube 12. The amplier 18 is so biased that the spot o n the cathode ray tube is deflected up to the top of the screen in the ab- .sence of a signal from the phototube. If the spot is not behind the opaque area of the mask, the phototube will detect it and deliver to the amplifier 18 a signal having a polarity such that the spot will be deflected downward. The combined effect of thev upward deflec- `it` will be appreciated that the output voltage signal -from the amplifier 18 maybe any desired function of the input voltage at the amplifier 20 as determined by 4 the shape of the upper edge of the mask 14. For the purpose of the pres'ent invention, in accordance with the requirements of Equation 10, the mask is formed with the upper edge conforming with a plotted curve of the value of the velocity gradient function dV Y Vdy Y as derived from bathothermograph data, against depth. With the voltage on the horizontal deflection plates varied in proportion to depth, the output voltage, and the voltage on the vertical deflection plates, is varied in proportion tothe velocity function Y dV Vdy

The output from the function generator 10 is fed to a first integrator 22 and second integrator 24 connected in cascade. The output `from the second integrator is therefore the second time integral of the quantity I l dV Vdy which according to the Equation l0 is the depth y of the ray.

The initial conditions of slope and depth of the ray are established in the first and second integrators respectively by means of adjustable control circuits 26 and 28. These circuits will hereinafter be described in more detail. The depth control circuit 28 estabis provided. The vertical deflection plates of the tube 30 are coupled to the output of the integrator 24 through a reflection circuit 32. The reflection circuit 32 may be `a full wave rectifier which maintains a constant polarity output regardless of changes of polarity of the output of the second integrator 24. This circuit provides for the condition where the depth of the ray becomes negative, that is, where the ray reaches the surface of the water and is reflected downward again.

A sweep circuit 34 is connected to the horizontal deflection plates of the cathode ray tube 30 to provide a linear time base, whereby a plot of depth as a function of time is traced on the face of the cathode ray tube 30. A conventional delay sweep circuit 36 is provided which may be connected by a switch 38 in place of the normal sweep 34 to the horizontal deflection plates of the cathode ray tube 30. The delay sweep makes it possible, .ifV desired, to enlarge and examine a portion of the ray trace on the cathode ray tube 30.

A synchronizing circuit 39, including a bistable multivibrator 40, -a monostable multivibrator 42 triggered by `the multivibrator 40, and a pulse shaper circuit 44, is

connected to the sweep circuits 34 and 36, as well as to the'initial angle'control circuit 26 and initial depth control circuit 28. This synchronizing circuit produces .an output pulse having a time duration of preferably $600 of a second, las determined by the recovery time of the monostable multivibrator 42, and a repetition frequency of 60 cycles per second as determined by the bistable multivibrator 40. These pulses from the output of the pulse shaper 44 trigger the initial control circuits 26 and 28 to reset the initial condition on the first integrator 22 and second integrator 24 once every so thatsuccessive rays, each with al ditierent initial slope, may be plotted. For this purposea motor drive, as inf dicated ,at 46, is provided for automatically shifting the initial angle'coutrol. f Y Referring to Fig. 2, the rStin'tegratOr circuit 22 .and

initial angle .control circuit 26 are shown in more detail.

The `integrator 22 is a common electronic type of integrator using a double-ended ampliiier `employing feedback to Vaccomplish the integration. Ihe 'input signal is coupled through series'resistors 48 and ,5.9 to. .the control grids of :a pair oflpentode .amplifier tubes 52 and 754. yThe cathodes of theampliiier tubes 52Y Vand ,S4- are connected together through a balance control potentifometer 56 to anegative voltage source;A ,T he plates and `screen grids -of,respective ampliiertubes 52 and 54 are `connected ina-conventional mannerv togsuitablepositive i.,

The output of :the tubes 52 and 54 are Vconnectedto cathode` followers including triodes 58 and `60j,the cathodes of Vwhich are connected to a negative voltage source through cathode resistors 62and 64 respectively. The.

output from the integrator 22 is derived across portions of the cathode resistors 62 and 64 to allow the output to be obtained at the proper D.C. level. VNegative feedback lis 'providedby the capacitorsV 66 and 68 which are respectively connected between the cathode of the cathode follower tube 58 and the control grid of the amplilier tube 52 `and the cathode of the `cathode Y'follower tube' 60 and control grid of the amplifier tube 54.

While the integrator has been disclosed and described as -a double-ended circuit, it will Yb'e understood that a singleended integrator circuit can be used.

hel operation of the integrator 22 can best be understood by consideringan initial charge Yplaced on the capacitor `66. In the absence of an inputsignal, this charge will leak oli through the loop consisting of the series resistor 48, the internal impedanceV of any driving circuit across the input to the integrator, andthe lcathode resistor62. 'This leakage constitu-tes a current and produces a change in voltage on `the control grid of the ampliiier tube 52. As la result, a voltage isjproduced at the cathode of thecat-hode follower tube 58 `which 'substantially cancels -the'loss in charge of the capacitor V66. Thus the ampliiier acts asa'n 'R-C integrator whose time constant `is greater thanithe R-C Vproduct by a facan input signal is applied lto the control Agrid off the arnpliiier tube S2, bywirtue ofthe action above described, thevoltag'e at the I cathode oifthe cathode Vfollower 58 is the integral of the input voltage from an initial D.C.

level ldeterrnined by lthe'initi'al charge `on Vthe condenser 66.

tor of approximately the gaini'fofthe ampliiier. When la synch pulse the output of the pulse shaper 44 by Y means of the initial angle control circuit 26.

t A fixed potential at the input Vend of the feedback capacitors deand 68, as Ycoupled to the control grids of the tubes S2 and 54, isV se'tA in the following manner. AV synch pulse 'from theioutp'ut of the pulse Shaper 44 is connected vthrough 'a cathode follower including a triode 7i! fand `cathode load potentiometer 72 tothe grids of a pair of triodes 74 vand 76 Ihaving their cathodes connected together to a iixed `negative potential source. The-plates :of the triodes .74 Yand A76 are connected respectively to the control grids of the amplifiers 52 and 54, so that these control grids are driven negative by the synchronizing pulse from the pulse Shaper 44. The potentialon the control grids of the tubes 52 and 54 is fixed during this interval by a pair of diodes 78 and 80 having their plates held at approximately-75 v. by a voltage divider including resistors 8 2 and 83. The cathodesof the' diodes 78 :and 80 `are connected to the `plates of the tniodes 74 and 76 limiting their drop in potential to -75 v.

A cathode follower including la triode 84 in the inte- `grator circuit 22 has its cathode -resistor 86 in common with the cathode circuits of the amplifier tubes 52 and 54. lThe grid of triode 84 is connected to a iixed potential of -75 y., so that the cathodes of therampliiier tubes are prevented yfrom dropping with the drop in potentialof the control grids below this potential. Thus the ampliiier tubes 52 and 54 `are cut oit by the synchronizer pulse. The circuit provided by the cathode follower tube 70, triodes 74 and 76, and diode limiters 78 and may be considered as a switch, actuated during the time of-a synchpulse, forconnecting one end of the feedback capacitors 66 and 68 to ixed potenti-al source of -75 v. v i

During the time the Vampliiier tubes 52 and 54 of the integrator circuit are thus cut 0E, the desired initial charge is placed ont'he capacitors 66 and 68by vconnecting an adjustable potential .to the other ends of these capacitors.

`are connected to load potentiometers 94 and 96 from ywhich a balanced output may be derived. The output may be deliberately unbalanced to simulate an unsymmetrical transducer. t

A pair of pentodes 98 and 100 have their plates connected to the plates ofthe amplifier tubes 52 and 54. FBhe control grids of the tubes 98 and 100 are connected by means of resistors 102 and 104 to a potentiometer 106 in the cathode circuit of fa Vcathode tollower 108. The synch signal from the pulse Shaper 44 is lfed to the control grid of the cathode follower 163 -so `as tobias the tubes 98 and 16%) conductive during the duration of the synch pulse. By connecting the screen grids. of the pentodes 98 and 100 to the output of the cathode followers and 92, during the'period of a sync-h pulse, the instantaneous potentials at the wiper contacts 87 and 83 determine respectively the potentials at lthe plates of the tubes 52 and 54 and hence the potentials at the cathodes of the cathode follower tubes S8 and 60. Thus the circuit including the cathode follower tubes 95) and 92, and pentodes 98 and i60, acts as a switch for momentarily connecting the 'feedback capacitors 66 and 68 to a variable source 88 of potential. v f

" By providing an 11:12 gear ratio between the motor 46 and potentiometer S8, and by operating the motor at the synchronous speed of one revolution per second, the same initial `condition is inserted into the integrator only once every twelve revolutions of the motor. Thus twelve times sixty or 720` traces, each With a different initial angle, are provided on the cathode ray screen 38. y

r[the second integrator 24 and the initial depth control circuit 2S are substantially identical to the circuits 22 and 26 as above described, except thata manual control of the potentiometer 88 is provided in place'of the motor l settingyof the ii-rst integrator determines the initial slope of the ray being vtraced'. Likewise, since the output of the second integrator is proportional to the depth y, the

phenomena, the origin, corresponding to the zero-depth,

zero-distance point, is placed in the Vcentenof the mask. The function is then plotted on one side ofthe y axis and repeated on the other side with symmetry about the origin, as shown in Fig. 3. However, -it will be appreciated that if one wishes to examine a deep Water problem in which the surface is not considered, the profile of the velocity function can be spread over the entire mask area and not just over one-half of it, It is desirable, in order to obtain quantitative results frornthe computer, that the mask always be plotted to the same scale. mask itself may be prepared in any one of several different ways. For example, the mask may be cut from black paper or may be made photographically.

From the above description it will be seen that various objects of the invention have been achieved by the Aprovision of a computer which will rapidly trace on a cathode ray tube a plurality Vof lines corresponding to ray paths emanating from a common source, but at different initial angles. If the horizontal and Vertical scale factors are equal (so as to present a linear tangent function), the resulting display on the cathode ray tube gives a visual picture of a computed sound field, for example, with the density of traces at any point being indicative of the predicted sound intensity. Generally the computer is used with an expanded depth scale since the horizontal distances involved are much greater than the depth. In this case the.ray trace is still accurately given but the density of the rays is not an accurate prediction of the sound intenslty pattern.

Since many changes could be made in the above construction and many apparently Widely different embodiments of this invention could be made without departing from the scope thereof, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

What is claimed is:

l. Apparatus for predicting the underwater sound pattern of a sound source, said apparatus comprising a pulse generator; a first integrator including an amplifier and a feedback capacitor coupling the output of the amplifier to the input; means for periodically setting an initial condition into the first integrator including a fixed source of potential, electronic switching means triggered by said pulse generator, the switching means momentarily coupling one end of the feedback capacitor of `said first integrator to the fixed source of potential with each pulse from said pulse generator, a variable source of potential,

means for continuously varying said last named source,

and second electronic switching means triggered by saidA .pulse generator, the switching means momentarily coupling the other end of the feedback capacitor of said first integrator to the variable source; a second integrator connected to the loutput of said first integrator and including an amplifier and a feedback capacitor coupling the output of the amplifier to the input; means for periodically setting an initial condition into the second integrator including a fixed source of potential, electronic switching means triggered Iby said pulse generator, the switching means momentarily coupling one end of the feedback capacitor of said second integrator to the fixed source of potential with each pulse from said pulse generator, a variable source of potential, and second electronic switching means triggered by said pulse generator, the switching means Vmomentarily coupling the other end of the feedback 8 capacitor of said second integrator to the variable source; an electronic function generator for producing an output signal who-se magnitude is a predetermined function of the magnitude of an input signal, the output of the func- ,tion generator being connected to the input of the first ,integrator and the input of the function generator being connected to the output of the second integrator; a sweep circuit synchronized with the output of the pulse generator;

and a cathode ray tube having horizontal and vertical deection means, the verticalV deflection means being coupled to the output of the second integrator and the horizontal deflection means being coupled to the output of the sweep circuit.

2. Apparatus for predicting the underwater sound pattern of a sound source, said apparatus comprising a pulse generator; a first integrator including an amplifier and a "feedback Ycapactior coupling the output of the amplifier to the input; means for setting an initial condition into the tor; a second integrator connected to the output of said -first integrator and including an amplifier and a feedback capacitor coupling the output of the amplifier to the input;

means for setting an initial condition into the second integrator including a fixed source of potential and a variable source of potential, and means triggered by said pulse generator for momentarily connecting opposite ends of the feedback capacitor of said second integrator respectively to said variable source and said xed source whereby a predetermined initial charge is placed on said capacitor; an electronic function generator for producing an output signal whose magnitude is a predetermined function of the magnitude of an input signal, the output of the function generator being connected to the input of the first integrator and the input of the function generator being connected to the output of the second integrator; a sweep circuit synchronized with the output of the 'pulse generator; a full wave rectier, and a cathode ray tube having horizontal and vertical deflection means, the

'vertical deecton means being coupled by said full wave rectifier to the output of the second integrator and the horizontal deflection means being couple to the output of the sweep circuit.

3. Apparatus for predicting the underwater sound pattern of a sound source, said apparatus comprising a pulse generator, a rst integrator including an amplifier and a feedback capacitor'coupling the output of the amplifier to the input, means triggered by the pulse generator for setting an initial condition into the first integrator by ansertlng 'a predetermined charge on the feedback capacitor thereof, a second integrator connected to the output of said first integrator and including an yamplifier and a feedback capacitor coupling the output of the amplifier to the input, means triggered by the -pulse generator for setting an initial condition into the second integrator by inserting a predetermined charge on the feedback capacitor thereof, an electronic function generator for producing an output signal whose magnitude is a predetermined function of the magnitude of Aan input signal, the output of the function generator being connected to the input of the first integrator and the input of the function generator being connected to the output of the second integrator, a sweep circuit synchronized with the output of the pulse generator, a full wave rectifier, and a cathode ray tube having horizontal and vertical deflection means, the vertical deflection means being coupled to the output of the second integrator by said full wave rectifier and the horizontal deflection means being coupled to the output of the sweep circuit.

4. A computer comprising a pulse generator; a first `integrator including capacitor; means for periodically set- Atingfan rinitial condition. into the'ifirst integrator including a ..fixed :sour`ce of= potential, electronic switching means triggered .by .said pulse generator, theV switching means momentarilycouplingf'one end `of .the capacitor Aof said firstinteg'ratorto said fixed source of .potential witheach- Y pulseffromfzrsaid tpulse generatorya.' variable source 'of potential, `means for continuouslygvaryinglsaid last Ynamedv source, and secondelectronic switching means triggered by said pufsiegenerat'or, the switching means momentarily said pulse "generator, a variablesjource' of potential, and

second electronic switching `means triggeredbyfsaid pulse generaton'the switching means momentarilycoupling the other end of the capacitor of said second integrator to said variable source; an electronic function generator for producing an output signal whose magnitude is -a predetermined function of the magnitude of an input signal, r

the output of the function generator being connected to the input of the first integrator and the input of the function generator being connected to the output of the second integrator; and means for indicating the change in output voltage of the second integrator as a function of time.

5. A sound ray computer comprising, a first integrator including capacitor; means for setting an initial condition into the first integrator including a fixed source of potential 'and a variable source of potential, and means for momentarily connecting opposite ends of the capacitor of said first integrator respectively to said variable source and said fixed source whereby a predetermined initial charge is placed on said capacitor; a second integrator adapted to receive the output of said first integrator and including a capacitor; means for setting an initial condi tion into the second integrator including afixed source of potential and a variable source of potential, and means for momentarily connecting opposite ends of the capacitor of said second integrator respectively to said variable source and said fixed source whereby a predetermined initial charge is placed on said capacitor; `an electronic function generator for producing an output signal whose magnitude is a predetermined function of the magnitude of `an input signal, the output of the function generator being connected to the input of the first integrator and the 'input of the function generator being connected to the output of the second integrator; a full Wave rectifier, and means synchronized with the operation of both said initial condition setting means for indicating the change in output Voltage of the second integrator as a function of time, said full wave rectifier interconnecting the output of the second integrator and the last-named means. 6.l A computer comprising, a first integrator including an amplifier ,and a feedback capacitor coupling the output of the amplifier to the input, means for setting an initial condition intov the first integrator by inserting a predetermined charge on the feedback capacitor of said first integrator, a second integrator adapted to receive the output of said first integrator and'including an arnplifier and 'a feedback capacitor coupling the output of the `amplifier to the input, means for setting an initial condition into the second integrator by inserting a predetermined charge on the feedback capacitor of said second integrator, an electronic function generator for producing an output signal whose magnitude is a predetermined function of the magnitude of an input signal, the output of the function generator being connected to the input of the first integrator and the input of the function generator being connected to the output of the second .Orincluding a fixed source f ,Y r11o v integrator, a full wave rectiner,gand means synchronized with the operation of bothsaid initial condition setting means :for indicating thechange in output voltage of the vsecond integrator as a function of time, said full wave rectifier interconnecting the output of the second inte-V grator and the last-named means.

7. A computer comprising, a first integrator including a capacitor, means for setting an initial condition into the rst integrator by inserting a predetermined charge on the capacitor of `sai`d first integrator, a second integrator adapte'dlto receive the'toutput of said'first integra- `tor'and including a' capacitor, means'forsettinglan initial condition.` into -thesecndr integrator by inserting a predetermined charge onthe capacitor of said second integrator, function generating means for producing an voutput voltage proportional -to the quantity in response to 'an input voltageproportional to 12W-here the dependent variable V is related empirically to the independent variable y, the output of the function gen- ,Y

erating means being connected to the input of the first integrator and the input of the function generating means being connected to the output of -the second integrator, a full Waverectifier, and means synchronized with the operation of both said initial condition setting means for rindicating the change in output voltage of the second integrator as a function of time, said full wave rectifier interconnecting the output of the second integrator and the last-named means.

8. Apparatus comprising, a first integrator, means for setting an -initial condition into the first integrator, a second integrator adapted to receive the output of said first integrator, means for setting an initial condition into the second integrator, an electronic function generator for producing an output signal whose magnitude is a predetermined function of the magnitude of an input signal, the output of the function generator being connected to the input of the first integrator and the input of the function generator being connected to the output of the second integrator, a full wave rectifier, -and means synchronized with the operation of both said initial condition setting means for indicating the change in output voltage of the second integrator as a function of time, said full wave rectifier interconnecting the output of the second integrator and the last-named means.

9. Computer means for plotting sound rays including a first integrator, a second integrator connected to the output of the first integrator, an electronic function generator for producing an output signal that is a predetermined function of an input signal, the output of the function generator being coupled to the input of the first integrator, the input of the function generator being coupled to the output of the second integrator, adjustable means coupled to each of the integrators for setting the initial condition of said'integrators, a sweep generator, afull wave rectifier, and a cathode ray tube having horizontal and Vertical defiection means, the vertical defiection means being coupled by said full wave rectifier to the output of the second integrator, the horizontal means being coupled to the output of the sweep generator, an

output pulse. derived from the sweep generator being coupled to said adjustable means for periodically restoring the integrators to their initial condition as set by said adjustable means.

10. Computer means for plotting sound rays including `a first integrator, a second integrator connected to the output of the first integrator, a function generator for producing an output that is a predetermined function of an input, the output of the function generator being coupled to the input of the first integrator, and the input of the function generator being coupled to the output of the second integrator, adjustable means coupled to each of the integrators for setting the initial condition of said integrators, a full Wave rectifier, and means synchronized with the operation of each said initial condition setting means for indicating the change in output of the second integrator as la function of time, said full wave rectier interconnecting the output of the second .integrator and the 1ast-namcd means.v

11. Computer `apparatus for solving the differential equation: Y

ci d V r @i Hy l i where V is empirically related to y according to measured data, said apparatus comprising means for generating an outputvoltage proportional to the quantity 1 di ,V dy y in response to an input voltage proportional to y as determined by said empirical relationship between V and y,

|a rst integrator coupled Y-to the output of said means, a second. integrator coupled to the output of the iirst integrator, the output of the second integrator being coupled to the input of` said means, means for setting initial conditions into said rst and second integrators, a full wave rectifier, and means synchronized with the operation of both said initial condition setting means for indicating the change in output of the second integrator with time, said full Wave rectier interconnect-ing the output of the second integrator and the |last-named means.

References Cited in the ile of this patent UNITED STATES PATENTS Shepherd et al. Sept. 30,119,152

OTHER REFERENCES --Proceedings of the National Electronics Conf. (Hancock), February l952, pages 228-234.

Electronic Analog Computers (Korn and Korn), June 1952, pages 46-497; 247-250; 343 and 344. Y Electronic Analog Computers (Korn and Korn), 1952; pages 226, 227, 289, 290 Iand 345. 

